Kobe is 2.07 metres tall.
Marcus is 1.79 metres tall.
Stephen is taller than Marcus by half the difference between Kobe's height and
Marcus's height.
How tall, in metres, is Stephen?
Optional working

Answer: x = -135.59

Step-by-step explanation:

20 = 0.694(x + 150)(2)

Step 1: Simplify both sides of the equation.

20 = 0.694 (x + 150)(2)

20 = 1.388x + 208.2 (use the distributive property)

20 = 1.388x + 208.2

Step 2: Flip the equation.

1.388x + 208.2 = 20

Step 3: Subtract 208.2 from both sides of the equation.

1.388x + 208.2 − 208.2 = 20 − 208.2

1.388x = −188.2

Step 4: Divide both sides by 1.388.

1.388x/1.388 = −188.2/1.388

x = −135.590778

Optional: Simplify

x = -135.59

The value of the sets are A ∩ ∅  = ∅ and A' ∪ U  = {f, g, h, p, q, r}.

Given: U = {f, g, h, p, q, r} and A = {g, p, r}

We are to find: (a)A ∩ ∅  and (b) A' ∪ U

(a) A ∩ ∅  

The symbol ∩ means intersection. This tells us what sets have in common. Also, the symbol ∅ means an empty set or null. That is a set that does not have any element

The intersection of a set with the empty set is the null set. Thus:

A ∩ ∅  = ∅

(b) A' ∪ U

The set U is called the universal set

A' means elements not in set A but in set U

The symbol ∪ means union, A' ∪ U will give a list of elements in A' and U combined without repetition. Thus:

A' ∪ U = {f, h, q} ∪  {f, g, h, p, q, r}  = {f, g, h, p, q, r}

Therefore, A ∩ ∅  = ∅ and A' ∪ U  = {f, g, h, p, q, r}. They should be entered into the boxes accordingly

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The dividend is 35286 and the divisor is 7. The value of the division is $540.8571

When dividing, it's important to note that the number that is being divided in this case 35286 is the dividend.

On the other hand, the number that is being divided by which is in this case 7 is the dividend.

The division will be:

= $35286 ÷ 7

= $540.8571

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After 35 years, Anthony's account is going to be worth $34193.12

The formula for the compound interest is given as

[tex]A = P(1 + r)^t[/tex]

Where we have the principal = 3000

the rate of interest = 7.2%

The period of time = 35 years

We have to input these values in the formula above so that we would have

A = 3000 ( 1 + 0.072)³⁵

A = 3000 x 11.398

= $34193.12

Hence we would have that after the period of 35 years, the account would be worth $34193.12

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Answer:

4(67 + 22)

Step-by-step explanation:

1. Find the greatest common factor(in this case it is 4)

2. Divide both 268 and 88 by 4 and you get 67 and 22

3. Put it in the requested format and you are left with 4(67 +22)

50 + 20x ≥ 250 is the inequality that can be used to find how many bags of candy Ms. Folk needs to buy to have at least 250 candies​.

How to solve equations in word problems?

Let x be the number of bags she bought:

50 + 20x ≥ 250

3x ≥ 200

x ≥ 200/3

x ≥ 66.67

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A few points (co-ordinates) for the given equations are :

(1,-1/2),(-1,1/4),(0,1),,(2,-1/4)

These points are called Coordinates, where the horizontal line denotes the x-axis and the verticle line is the y-axis.

Each point is identified by both x and y coordinates. A point's x-coordinate is a value that indicates how far the point is from the horizontal or x-axis origin.

y denotes the distance of the point on the vertical line from the origin

x denotes the distance of the point on the horizontal line from the origin

In the given equation y=-1/3x-1

We can substitute x with any integer (i.e any number among the positive or negative numbers)

Putting, x=1 in the given equation we get

y=-1/(3x1)-1

⇒ y=-1/3-1

⇒y=-1/2

Thus the coordinate when x=1 is (1,-1/2)

Similarly by putting x=0, 1, 2, -1 ;we get the following co-ordinates respectively

(0,1), (1,-1/2), (2,-1/4),(-1,1/4)

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Answer:

Scalene

Step-by-step explanation:

a scalene triangle has three sides different angles none of its sides are equal in length

Answer:

A scalene triangle or quadrilateral has no equal sides.

Answer:

- 90

Step-by-step explanation:

substitute x = - 2 into f(x)

f(- 2) = 3[tex](-2)^{5}[/tex] - [tex](-2)^{4}[/tex] - 6(- 2) + 10

        = 3(- 32) - (16) + 12 + 10

        = - 96 - 16 + 22

        = - 112 + 22

        = - 90

[tex]{ \boxed{ \sf{f( - 2) = - 90}}}[/tex]

Step-by-step explanation:

[tex]{ \red{ \tt{f(x) = {3x}^{5} - {x}^{4} - 6x + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = 3( { - 2})^{5} - ( { - 2})^{4} - 6( - 2) + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = 3( - 32) - 16 + 12 + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = - 96 - 16 + 12 + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = - 112 + 22}}}[/tex]

[tex]{ \green{ \boxed{ \bold{f( - 2) = - 90}}}}[/tex]

By using the concept of differentiation, it can be calculated that

value of P is -2 and value of Q is 1

What is differentiation?

Differentiation is the process where  the instantaneous rate of change of function can be calculated based on one variable. Differentiation is a very important tool in calculus

Here differentiation is used

f(x) = [tex]x^2y[/tex]

[tex]df = 2xydx+x^2dy[/tex]

Here P = 2xy, Q = [tex]x^2[/tex]

At x = 1, y = -1

P = 2(1)(-1) = -2

Q = [tex](-1)^2[/tex] = 1

So value of P is -2 and value of Q is 1

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We will need 7 quart package if we want 62 strawberries

What is division?

Division is one of the basic arithmetic computation which divide a value in equal sets of smaller values. The other basic arithmetic computations are addition, subtraction, multiplication. We use long division method to find the quotient and remainder.

We are given that there are 9 strawberries in a quart package

Also we want 62 strawberries

Then how many quart will be required

Now we perform division to find the number of quart

62/9 = we get a value of 8.88

Which is very close to nine

Hence we will need 9 quart packages if we want 62 strawberries

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If a transversal intersects two lines such that a pair of alternate interior angles is equal , then the two lines are parallel.

What do you mean by traversal line?

A transversal is a line that, at two different locations in the geometry, cuts through two lines in the same plane. Various sorts of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.

What do you mean by angle?

An angle is defined as the figure, in which two rays meet at a common point called the vertex. The angle is denoted using the symbol “∠”.

From the figure,

x + 1 = 180°

y + 2 = 180°

Adding above equations,

x + y + 1 + 2 = 360°

Given ,

x + y = 1 +2

x + y + x + y = 360°

2(x + y) = 360°

x + y = 180°

Angles made on same side of transversal is supplementary . So the lines are parallel.

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Answer: the coefficient of the 6th term of (2x - 7)⁹ is -33882912

Step-by-step explanation:

[tex](2x-7)^9[/tex]

In this problem we use the following formula:

                              [tex](a+b)^n=\sum\limits _{k=0}^nC_n^ka^{n-k}b^k[/tex]

a=2x         b=-7        n=9

The 1th term of (2x-7)^9 is k=0

The 2th term of (2x-7)^9 is k=1

The 3th term of (2x-7)^9 is k=2

..........................................................

The 6th term of (2x-7)^9 is k=5

Hence,

[tex]\displaystyle\\C_9^5(2x)^{9-5}(-7)^5=\\\\\frac{9!}{(9-5)!*5!}(2x)^4(-7)^5 =\\\\\frac{9!}{4!*5!} 2^4x^4(-7)^5=\\\\126(16)(-16807)(x^4)=\\\\=-33889212x^4[/tex]

- 33889212x⁴ is the coefficient of the 6th term in  binomial theorem .

What is binomial theorem?

( 2x - 7 )⁹

compare with formula

a = 2x    b = - 7  n = 9

The 1th term of (2x-7)^9 is k=0

The 2th term of (2x-7)^9 is k=1

The 3th term of (2x-7)^9 is k=2

...................................................

The 6th term of (2x-7)^9 is k=5

hence

⁵C₉( 2x )⁹⁻⁵ ( - 7)⁵  = 9!/( 9-5)!* 5! (2x)⁴( -7)⁵

                            = 9!/4! * 5! 2⁴x⁴( -7)⁵

                              = 126(16) ( - 16807 )(x)⁴

                              =  - 33889212x⁴

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For the given two sets A and B, the set B is equal to A.

Set:

A set is the collection of well-defined objects or elements. It is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}.

Given.

Here we have the two sets

A =  {piano, guitar, violin) and

B = (guitar, piano, violin)

Now, we need to find the relation between  B and A.

While we looking into the given sets,

Set A has 3 elements in it and

Set B has 3 elements in it.

So, the size of both sets are equal.

And now we have to looking at the elements in it.

While we checking the elements, instead of the order both have the same elements.

Therefore, the set B is equal to set A.

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Answer:

Your answer would be 2.1.

Step-by-step explanation:

The square root of 3 is:

1.73205080757

Then since 1/3 is equal to 0.33, I added 0.33 to the square root of 3 to get:

2.06205080757

Then, I rounded it:

2.1

The speed of the aircraft is 682 mph

Given that: A speed of 60 mph is equal to 88 ft/sec

If an aircraft travels at a speed of 1000 ft/sec, the speed to the nearest mile per hour can be calculated by using the unit  ratio of

of mph to ft/s, that is:

60/88 = m/1000

m = 6x1000/ 88 = 60000/88 = 682 mph

Therefore, the speed of the aircraft to the nearest mile per hour is 682 mph

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We can conclude that (C) Gibbons will live in a building that is similar to the Chimpanzee's rectangular house.

So, observe the given shapes on the graph:

Therefore, we can conclude that (C) Gibbons will live in a building that is similar to the Chimpanzee's rectangular house.

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The partial fraction is proved.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

=3x²+8x+4/(x²-4)(3x-2)

=3x2+8x+4/(x2-4)(3x-2)

= 3x2+6x+2x+4/(x2-4)(3x-2)

=3x(x+2)+2(x+2)/(x2-4)(3x-2)

Hence proved, l.h.s = r.h.s

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Answer:

7/12

Step-by-step explanation:

12/12 - 5/12 = 7/12

Answer:

row-echelon form

Step-by-step explanation:

Matrixes are commonly used to do Gaussian elimination. By reducing the need to manually specify the parameters at each step, this strategy decreases the work required to obtain the solutions. A system of equations equations is solved using the Gauss elimination method. Let's review the definitions of these equation systems. A set of linear equations with numerous unknown components is defined as a system of linear equations. Unknown factors can be found in various equations, as we all know.

The differentiation of [tex]e^x[/tex] is [tex]\frac{d}{dx}(e^x) =e^x[/tex]. Hence, proved,

Given that, [tex]\frac{d}{dx}(e^x) =e^x[/tex].

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

Differentiate using the Exponential Rule which states that [tex]\frac{d}{dx}(a^x)[/tex] is [tex]a^xln(a)[/tex] where [tex]a=e.e^x[/tex]

So, now [tex]\frac{d}{dx}(e^x) =e^x[/tex]

The differentiation of [tex]e^x[/tex] is [tex]\frac{d}{dx}(e^x) =e^x[/tex]. Hence, proved,

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A' - (-1,4)

B' - (-1,8)

C' - (-5,4)

hope this helps

The inequality will be represented by p ≥ 33 for at least 15 points.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Mark must score at least 11 points to have an average of 10 points per game.

The average of a set of data is its sum, divided by the number of data points in the set. If p is the number of points Mark scores in his next game, and he wants his average at least 15, then the relation is ...

 (8+14+10+20+5++p)/6 ≥ 15

 57 +p ≥ 90 . . . . . . . . . multiply by 6 and simplify

 p ≥ 33

Mark must score at least 33 points in the next game to average at least 15 points per game.

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The equation of the line representing the given situation is y = (3/4)x , the graph of the equation is shown below .

In the question ,

it is given that ,

a refreshment stand makes 3 large serving of frozen yogurt from 4 pints .

also given that number of pints is represented by x - axis .

the number of servings is represented by y - axis  .

the equation of the line is represented by y = mx + c .

we get c = 0, because at 0 pint there is no servings

hence , the  equation becomes y [tex]=[/tex] mx .

According to the question ,

3 = m*4

m = 3/4 .

Substituting the value of m in the equation , we get

y = (3/4)x

the graph of the equation is shown below .

Therefore , The equation of the line representing the given situation is y = (3/4)x .

The given question is incomplete , the complete question is

A refreshment stand makes 3 large servings of frozen yogurt from 4 pints. Graph the line and then write its equation. Let the x-axis represent the number of pints and the y-axis represent the number of servings. Use only fractional form, if necessary.

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The percentage of the cupcakes that had sprinkles if 39 out of the 52 cupcakes had sprinkles on top is 75%.

A division by 100 results in a percentage, often known as a percent. A percentage denotes a component of a total sum and indicates "per 100". For example, 45% represents 45 out of 100. Calculating a percentage is the process of determining a whole's proportion in terms of 100.

Given:

The total no cupcakes = 52,

The no of sprinkled cupcakes = 39,

Percentage of sprinkled cupcakes = The no of sprinkled cupcakes / The total no cupcakes × 100

Percentage of sprinkled cupcakes = 39 / 52 × 100

Percentage of sprinkled cupcakes = 75%

Therefore, the percentage of the cupcakes that had sprinkles if 39 out of the 52 cupcakes had sprinkles on top is 75%.

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Answer:

the answer according to my solution is 06